Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $$100.$ The materials cost for a

standard diamond is $$40.$ The fixed costs incurred each year for factory upkeep and administrative expenses are $$200,000.$ The

machinery costs $$1$ million and is depreciated straight$-$line over $10$ years to a salvage value of zero.

a$.$ What is the accounting break$-$even level of sales in terms of the number of diamonds sold?

Note: Do not round intermediate calculations.

b$.$ What is the NPV break$-$even level of sales assuming a tax rate of $21\%,$ a $10-$year project life, and a discount rate of $12\%?$

Note: Do not round intermediate calculations. Round your answer up to the nearest whole unit.